General Information:

Here the words "them" and "their" refer to those who were sick.

even handkerchiefs and aprons that had touched him were taken to the sick and

This can be stated in active form. Alternate translation: "when they took to sick people even handkerchiefs and aprons that had touched Paul"

Possible meanings are 1) these were cloth items that Paul had touched or 2) these were cloth items that Paul had worn or used.

cloths worn around the head

clothing worn on the front of the body to protect the clothes of people

This refers to sick people. Alternate translation: "sick people" or "those who were sick" (See: rc://en/ta/man/translate/figs-nominaladj)

"those who were sick became healthy"